"We have / some more / bad news" is how you would break up the sentence. We don't read it as "We have some more-bad news".
You're correct, we don't say something is "more-bad"; it's always "worse".
The difference between your two options is that "some more bad news" means the bad news is more of the same. "Some worse news" means that the new information outdoes the bad news already known.